International Journal of Modern Physics D

An important concept in Physics is the notion of an isolated system. It is used in many different areas to describe the properties of a physical system which has been isolated from its environment. The interaction with the “outside” is then usually reduced to a scattering process, in which incoming radiation interacts with the system, which in turn emits outgoing radiation.

In Einstein’s theory of gravitation, isolated systems are modeled as asymptotically flat spacetimes. They provide the appropriate paradigm for the study of gravitational waves and their interaction with a material system or even only with themselves. In view of the emerging era of gravitational wave astronomy, in which gravitational wave signals from many different astrophysical sources are detected and interpreted, it is necessary to have a foundation for the theoretical and numerical treatments of these signals.

Furthermore, from a purely mathematical point of view, it is important to have a full understanding of the implications of imposing the condition of asymptotic flatness onto solutions of the Einstein equations. While it is known that there exists a large class of asymptotically flat solutions of Einstein’s equations, it is not known what the necessary and sufficient conditions at infinity are that have to be imposed on initial data so that they evolve into regular asymptotically flat spacetimes. The crux lies in the region near spacelike infinity $i^0$ where incoming and outgoing radiation “meet”.

In this paper, we review the current knowledge and some of the analytical and numerical work that has gone into the attempt to understand the structure of asymptotically flat spacetimes near spacelike and null-infinity.

Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the canonical commutation relations and hence quantum mechanics at the Planck scale. The corresponding modification of classical mechanics is usually considered by replacing modified quantum commutators by Poisson brackets suitably modified in such a way that they retain their main properties (antisymmetry, linearity, Leibniz rule and Jacobi identity). We indicate that there exists an alternative interesting possibility. Koopman–von Neumann’s Hilbert space formulation of classical mechanics allows, as Sudarshan remarked, to consider the classical mechanics as a hidden variable quantum system. Then, the Planck scale modification of this quantum system naturally induces the corresponding modification of dynamics in the classical substrate. Interestingly, it seems this induced modification in fact destroys the classicality: classical position and momentum operators cease to be commuting and hidden variables do appear in their evolution equations.

In this paper, we discuss possible three early eras of the universe in the theoretical context of the Galilean cosmology. The first phase is a slow-roll inflation phase in which the friction term in the equations of motion dominates over the kinetic term. This is the initial vacuum state leading to quasi-de Sitter expansion. The second phase is where the cosmological perturbations are supposed to be generated. In this phase, the friction term is supposed to be negligible which leads to the appearance of the Galileon inflation field. The third phase is the reheating phase in the standard cosmology, where the oscillations of a canonical scalar field in the model lead to this phase. These three eras for the early universe are shown by a single master equation of the theory. However, we compute observational indices (the scalar spectral index parameter and the tensor-to-scalar ratio) for the era where the era that the perturbations are produced. Finally, we compare viability of the theoretical findings with the latest Planck observational data.

We study the gravitational waves (GWs) in modified Gauss–Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is equal to the speed of light. An additional massive scalar mode appears in the propagation of the GWs. To find phenomena beyond the general relativity, the scalar mode mass is calculated as a function of the background curvature in some typical models.

In this paper, we discuss the behavior of coordinate-time dependent lapse function of FLRW metric of an accelerated expanding universe in the de Rham–Gabadadze–Tolley massive gravity theory. Physically, this function is considered to connect a general observer coordinate-time to the related proper-time and also to another normal observer under specific condition. We find that in the standard dRGT formalism, the corresponding lapse function can exhibit unphysical behavior in the parameter space region with a negative cosmological-constant-like term. To solve this problem, we reconsider the cosmological constant energy density which induces negative pressure. It turns out that this setup could overcome the existence of singular and negative square lapse function in the related parameter space and restore all the parameter space to admit only the accelerated expanding universe model.

Killing symmetries are revisited in $d=5$ bulk geometric torsion (GT) perturbation theory to investigate the perihelion precession. Computation reveals a nonperturbative (NP) modification to the precession known in General Relativity (GR). Remarkably the analysis reassures our proposed holographic correspondence between a perturbative GT in bulk and a boundary GR coupled to $B_2\wedge F_2$. In fact, the topological correction is sourced by a non-Newtonian potential in GR and we identify it with an “electro-gravito” (EG) dipole. Interestingly, the dipole correction is shown to possess its origin in a $4$-form underlying a propagating GT and leads to a NP gravity in $d=4$.

For the accurate understanding of compact astrophysical objects, the Tolmann–Oppenheimer–Volkoff (TOV) equation has proved to be of great use. Nowadays, it has been derived in many alternative gravity theories, yielding the prediction of different macroscopic features for such compact objects. In this work, we apply the TOV equation of the energy–momentum–conserved version of the $f(R,T)$ gravity theory to strange quark stars. The $f(R,T)$ theory, with $f(R,T)$ being a generic function of the Ricci scalar $R$ and trace of the energy–momentum tensor $T$ to replace $R$ in the Einstein–Hilbert gravitational action, has shown to provide a very interesting alternative to the cosmological constant $\mathrm{\Lambda }$ in a cosmological scenario, particularly in the energy–momentum conserved case (a general $f(R,T)$ function does not conserve the energy–momentum tensor). Here, we impose the condition ${\nabla }^{\mu }{T}_{\mu \nu }=0$ to the astrophysical case, particularly the hydrostatic equilibrium of strange stars. We solve the TOV equation by taking into account linear equations of state to describe matter inside strange stars, such as $p=\omega \rho$ and $p=\omega (\rho -4B)$, known as the MIT bag model, with $p$ the pressure and $\rho$ the energy density of the star, $\omega$ constant and $B$ the bag constant.

Recently, it was shown that, in an effective description motivated by loop quantum gravity, singularities of the Kruskal spacetime are naturally resolved [A. Ashtekar, J. Olmedo and P. Singh, Phys. Rev. Lett. 121 (2018) 241301; A. Ashtekar, J. Olmedo and P. Singh, Phys. Rev. D 98 (2018) 126003]. In this paper, we explore a few properties of this quantum corrected effective metric. In particular, we (i) calculate the Hawking temperature associated with the horizon of the effective geometry and show that the quantum correction to the temperature is completely negligible for macroscopic black holes, just as one would hope; (ii) discuss the subtleties associated with the asymptotic properties of the spacetime metric, and show that the metric is asymptotically flat in a precise sense; (iii) analyze the asymptotic fall-off of curvature; and, (iv) show that the ADM energy is well defined (and agrees with that determined by the horizon area), even though the curvature falls off less rapidly than in the standard asymptotically flat context.

We study $\alpha$-attractor models with both E-model and T-model potential in an extended Nonminimal Derivative (NMD) inflation where a canonical scalar field and its derivatives are nonminimally coupled to gravity. We calculate the evolution of perturbations during this regime. Then by adopting inflation potentials of the model we show that in the large $N$ and small $\alpha$ limit, the value of the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ are universal. Next, we study reheating after inflation in this formalism. We obtain some constraints on the model’s parameter space by adopting the results with Planck 2018.